The Google ads service places ads based upon words within the page for which it's placing the ads. On this site, we talk about Christianity, Islam, and other religions. When we do that, the ads for those pages will often be for those sorts of religious sites.

Click it and have it open in another tab. Chances are good that the site that placed the ad has to pay for every click through they get. End result: religion-based companies, sites and services pay for Atheist Nexus' hosting fees.

AdChoices is configurable to an extent but AN moderators would need to look at the configuration to change it. Users can't change it.